As it happens, the applicability of the slow-roll condition is closely
connected to the condition for inflation to take place, and in many
contexts the conditions can be regarded as equivalent. Let's quickly
see why.

The inflationary condition
> 0 is satisfied for a much
wider range of behaviours than just (quasi-)exponential expansion. A
classic example is power-law inflation
atp for p > 1,
which is an exact solution for an exponential potential

(30)

We can rewrite the condition for inflation as

(31)

where the last manipulation uses the slow-roll approximation. The
final condition is just the slow-roll condition
< 1, and
hence

Inflation will occur when the slow-roll conditions are satisfied
(subject to some caveats on whether the `attractor' behaviour has been
attained [8]).

However, the converse is not strictly true, since we had to use the
SRA in the derivation. However, in practice

The last condition arises because unless the curvature of the
potential is small, the potential will not be flat for a wide enough
range of .